Both refer to a large amount. "Much" can only be used with uncountable nouns. "a lot of" can be used with nouns you CAN or CAN NOT count: - There are a lot of students in the classroom. (24 students - countable noun) - The old lady has a lot of cats. (11 cats - countable noun) - There's a lot of snow on the ground. (uncountable noun) - I like to put a lot of salt on my food. (uncountable noun) "much" is ONLY used with nouns you CAN NOT count: - There isn't much milk left. (uncountable noun) - I have too much work to do. (uncountable noun) - There is so much to learn. (uncountable noun) - I love you very much. (uncountable noun)

They mean the same thing but are used differently. The best I can do is give you some examples. "Did you earn a lot of money from your car sale?" "Did you earn much money from your car sale?' Both are correct. The first implies that the speaker thinks a great deal of money might have been earned. The second one implies that the speaker thinks that maybe not very much money was earned. It is a subtle difference. "Do you like a lot of different kinds of flowers?" "Do you like much different kinds of flowers?" Both are OK. The first is asking if I like many varieties of flowers. The second is asking if I like flowers that are very different from each other, or very different from the flowers we are looking at. Again, a subtle difference. " A lot of" is also more colloquial.